This invention relates to methods for arranging or adapting fuzzy controllers or a system of interlinked fuzzy controllers having at least two input variables and an output variable in which the controller or system has input membership functions with which truth values of linguistic values for the input variables are determined, has a control mechanism in which truth values for the output variable are determined from the truth values for the input variables, and has output membership functions with which the values of the output variable are determined from the truth values for the output variable.
Fuzzy controllers are used when process-specific strategies based on experience, which may be formulated in everyday speech as IF-THEN rules, are to be embodied in algorithms which are capable of being automated. As is known from numerous publications, fuzzy controllers constitute nonlinear, multivariable characteristic map controllers whose static transfer properties depend essentially on the number, position and shape of the membership functions and on the formulation of the linguistic control mechanism. The multiplicity of input variable results in a considerable amount of randomness in the knowledge-based setting-up of fuzzy controllers. Right from the setting of the objective, it is obvious that the design of a fuzzy controller differs fundamentally from that of a conventional controller. Parametric process models and mathematically safeguarded controller design methods are at the foreground of conventional control technology and fuzzy controllers are primarily concerned with the operationalization of such available knowledge.
The normal procedure in the conversion of available knowledge to algorithms is that, following the definition of the input and output variables of the fuzzy controllers, a fuzzy partitioning of the numerical values by means of linguistic values and a positioning of the membership functions for the input and the output variables is carried out. This is followed by the formulation of the expert knowledge as IF-THEN rules and the selection of a suitable defuzzification method. If the necessary expert knowledge is not available, methods for fuzzy controller design or adaption must be used.
In the publication "Lernverfahren fur Fuzzy-Regler", [Learning methods for fuzzy controllers], Automatisierungstechnische Praxis 37 (1955) 7, pages 10-20, a learning process for fuzzy controllers using a classification based on measurement data sets is described. The basis for the method is a classifying statement for the extraction from fuzzy controllers of data sets which in each case consists of an output variable and the associated input variables. According to the basic idea, all data sets constitute elementary rules, the data distribution determines the position of the membership functions and the elementary rules of greatest relevance define the final control base. The membership functions for the input and output variables are initially assumed to be given in the known method. All values from an exemplary data set are fuzzified using the membership functions and are categorized or classified in accordance with their degree of membership. By interlinking the degrees of membership according to the Min operation of fuzzy logic, rules of different relevance are formed. In the process, all those terms which have a degree of satisfaction greater than 0 are taken into account.
The disadvantage of this iterative method is in particular that the memory requirement is very high, since the value combinations of the input and output variables over the entire duration of the adaptation are needed and the adaptation itself lasts for a very long time.